The revenue accrued for the use of the transmission system is used to recover the cost of planning, operation and maintenance and must be paid by generators and loads, which are the users of the system. One of the main challenges is how to establish the best way to allocate these costs to generators and loads. In developing countries, like Brazil, fast generation and transmission expansion triggered by a sharp demand growth, can cause significant volatility and dispersion among agents transmission tariffs. These effects can create an unsafe environment for new investors in generation. In order to face this problem, this dissertation proposes a new transmission cost allocation method that utilizes an approach based on the min-max optimization technique, and on the nodal method used in Brazil. The idea behind the utilization of min-max method is that the agents with the worst tariffs should have priority in the tariff optimization process. Thus, the objective is to provide an equitable solution and, consequently, a reduction of the dispersion and volatility of the tariffs over time, when new transmission or generation assets are incorporated into the system. The results presented for IEEE 24 bus and IEEE 118 bus systems indicate that the proposed approach gives less-dispersed tariffs compared with other existing methods, but keeping the desirable features of the traditional nodal method. The proposed method also shows less volatility in tariffs if changes (like different generation dispatches) are made to the system.